Question

Ethylene can be produced in a continuous dehydrogenation process at steady state. Calculate the molar composition of the product gas and the fractional yield of ethylene.

Options:
a) Not Applicable
b) Need More Data
c) Calculable
d) Incomplete Information

Answer 1

You calculate the production of ethylene by converting the mass of ethane to moles, using the molar masses, and then converting back to kilograms for ethylene considering the stoichiometry of the reaction and 100% yield, resulting in approximately 932.25 kg of ethylene.

Step-by-step explanation:

To calculate how many kilograms of ethylene are produced from the pyrolysis of 1.000 × 10³ kg of ethane with a 100.0% yield, we first need to know the molar masses of ethane (C₂H₆) and ethylene (C₂H₄). The molar mass of ethane is 30.07 g/mol, while the molar mass of ethylene is 28.05 g/mol.

Assuming a 100% yield in the reaction C₂H₆ → C₂H₄ + H₂, for each mole of ethane used, 1 mole of ethylene is produced. Convert the mass of ethane to moles and then calculate the corresponding mass of ethylene using the ratio of their molar masses (C₂H₄/C₂H₆).

1. Calculate moles of ethane: (1.000 × 10³ kg ethane) × (1000 g/kg) × (1 mol/30.07 g) = 33,233.4 mol ethane.
   
2. Since the yield is 100%, moles of ethylene produced = moles of ethane used = 33,233.4 mol.
   
3. Calculate kilograms of ethylene: (33,233.4 mol) × (28.05 g/mol) × (1 kg/1000 g) ≈ 932.25 kg ethylene.

Therefore, 932.25 kg of ethylene is produced from the pyrolysis of 1.000 × 10³ kg of ethane at a 100.0% yield.